Universal Cell Algebra Geometry, Operators, and the Curvature Architecture of the Eukaryotic Cell

Here is the description for UCA on Zenodo: Title: Universal Cell Algebra: Geometry, Operators, and the Curvature Architecture of the Eukaryotic Cell Author: Abdon EC Bishop Date: March 16, 2026 License: CC-BY 4.0 Description: This work introduces Universal Cell Algebra (UCA), a mathematical framework that models the eukaryotic cell as a curvature-closed, operator-driven, spectral dynamical system. The central claim is that the genome is not a symbolic sequence but a curvature-bearing two-dimensional manifold acted upon by four operators — a chromosome rotor, a replication operator, a telomeric boundary operator, and a curvature Laplacian. All genetic processes are governed by a single global invariant: the total Gaussian curvature of the modular genetic surface. The framework proves that genes are polynomial field objects, proteins are their analytic continuations, replication is curvature doubling, and the mtDNA D-loop is the spectral ground state of the entire genetic surface. A Fundamental Theorem establishes the equivalence of five conditions: dynamic stability, global curvature conservation, isometric operator action, spectral anchoring, and curvature-preserving closure. The framework connects to nuclear physics, cancer cell arithmetic, and the structure of spacetime. A companion paper applying the same geometric architecture to nuclear stability is available at https://doi.org/10.5281/zenodo.18615174 Keywords: curvature geometry, operator algebra, eukaryotic cell, Gaussian curvature, chromosome rotor, spectral theory, mtDNA, replication dynamics, cancer, modular arithmetic, differential geometry Paste that in and you are done.